It would be impossible to throw a disc forward if it was rotating on the Z axis, a disc thrown flat rotates on the Y axis.

That xylo in the video above rotates on the Z axis though.

????

The definition of your reference frame is arbitrary. Also convention normally dictates that z denote the vertical axis. The way we've been talking, we've been using a moving reference frame and defining the z-axis to be normal to the top of the disc.